MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nic-mpALT Unicode version

Theorem nic-mpALT 1505
Description: A direct proof of nic-mp 1504. (Contributed by NM, 30-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-jmin
nic-jmaj
Assertion
Ref Expression
nic-mpALT

Proof of Theorem nic-mpALT
StepHypRef Expression
1 nic-jmin . 2
2 nic-jmaj . . . . 5
3 df-nan 1344 . . . . . 6
4 df-nan 1344 . . . . . . 7
54anbi2i 694 . . . . . 6
63, 5xchbinx 310 . . . . 5
72, 6mpbi 208 . . . 4
8 iman 424 . . . 4
97, 8mpbir 209 . . 3
109simprd 463 . 2
111, 10ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  -/\wnan 1343
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-nan 1344
  Copyright terms: Public domain W3C validator